Research Projects

The following papers summarize work that use Property Fund data.

Rating Endorsements using Generalized Linear Models

by Edward W. (Jed) Frees and Gee Lee. Scheduled to appear in Variance, the flagship journal of the Casualty Actuarial Society. See the blog by Gee for additional information about this work.

Abstract. Insurance policies often contain optional insurance coverages known as endorsements. Because these additional coverages are typically inexpensive relative to primary coverages and data can be sparse (coverages are optional), rating of endorsements is often done in ad hoc manner after a primary analysis has been conducted. This paper describes a study of the Wisconsin Local Government Property Insurance Fund where it is desirable to have a formal mechanism for rating endorsements. Our goal is to provide prediction algorithms that are transparent and that promote equity among policyholders by determining rates that reflect the appropriate level and amount of uncertainty of each risk. To accommodate potentially conflicting goals of data complexity and algorithmic transparency, we utilize shrinkage techniques to moderate the e.ffects of endorsements with penalized likelihoods. We .find that the rating algorithms using shrinkage techniques have a predictive accuracy that are comparable to unbiased generalized linear model techniques and provide relativities for endorsements that are consistent with sound economic, risk management, and actuarial practice.

Multivariate Frequency-Severity Regression Models in Insurance

by Edward W. (Jed) Frees , Gee Lee, and Lu Yang. This paper appeared in Risks 2016, 4(1), 4. (Risks is an open access journal, available at http://www.mdpi.com/journal/risks).

Abstract: In insurance and related industries including healthcare, it is common to have several outcome measures that the analyst wishes to understand using explanatory variables. For example, in automobile insurance, an accident may result in payments for damage to one’s own vehicle, damage to another party’s vehicle, or personal injury. It is also common to be interested in the frequency of accidents in addition to the severity of the claim amounts. This paper synthesizes and extends the literature on multivariate frequency-severity regression modeling with a focus on insurance industry applications. Regression models for understanding the distribution of each outcome continue to be developed yet there now exists a solid body of literature for the marginal outcomes. This paper contributes to this body of literature by focusing on the use of a copula for modeling the dependence among these outcomes; a major advantage of this tool is that it preserves the body of work established for marginal models. We illustrate this approach using data from the Wisconsin Local Government Property Insurance Fund. This fund offers insurance protection for (i) property; (ii) motor vehicle; and (iii) contractors’ equipment claims. In addition to several claim types and frequency-severity components, outcomes can be further categorized by time and space, requiring complex dependency modeling. We find significant dependencies for these data; specifically, we find that dependencies among lines are stronger than the dependencies between the frequency and average severity within each line.

Insurance Portfolio Risk Retention

by Edward W. (Jed) Frees. This paper has been submitted for publication.

Abstract. In this paper, I introduce a statistic for managing a portfolio of insurance risks. This tool is based on changes in the risk profile when changes in a risk parameter, such as a deductible, coinsurance, or upper policy limit, are made. I refer to the new statistic as a risk measure relative marginal, or RM², for short, change. By examining data from the Wisconsin Local Government Property Fund, I show how RM² changes can be used by a policyholder to select an effective risk mitigation strategy. I also show how it can be used by an insurer to identify the "best" and "worst" risks in terms of opportunities for risk management. The RM² changes reflect the underlying dependence structure of risks; I use an elliptical copula framework to demonstrate the sensitivity of risk mitigation strategy to the dependence structure.

Pair Copula Constructions for Semicontinuous Longitudinal Data with Application to Insurance Experience Rating

by Peng Shi and Lu Yang. This paper has been submitted for publication.

Abstract. In non-life insurance, insurers use experience rating to adjust premiums to reflect policyholders’ previous claim experience. Performing prospective experience rating can be challenging when the claim distribution is complex. For instance, insurance claims are semicontinuous in that a fraction of zeros is often associated with an otherwise positive continuous outcome from a right-skewed and long-tailed distribution. Practitioners use credibility premium that is a special form of the shrinkage estimator in the longitudinal data framework. However, the linear predictor is not informative especially when the outcome follows a mixed distribution.

In this article, we introduce a mixed vine pair copula construction framework for modeling semicontinuous longitudinal claims. In the proposed framework, a two-component mixture regression is employed to accommodate the zero inflation and thick tails in the claim distribution. The temporal dependence among repeated observations is modeled using a sequence of bivariate conditional copulas based on a mixed D-vine. We emphasize that the resulting predictive distribution allows insurers to incorporate past experience into future premiums in a nonlinear fashion and the classic linear predictor can be viewed as a nested case.

In the application, we examine a unique claims dataset of government property insurance from the state of Wisconsin. Due to the discrepancies between the claim and premium distributions, we employ an ordered Lorenz curve to evaluate the predictive performance. We show that the proposed approach offers substantial opportunities for separating risks and identifying profitable business when compared with alternative experience rating methods.